Fast Marching based Tissue Adaptive Delay Estimation for Aberration Corrected Delay and Sum Beamforming in Ultrasound Imaging

Conventional ultrasound (US) imaging employs the delay and sum (DAS) receive beamforming with dynamic receive focus for image reconstruction due to its simplicity and robustness. However, the DAS beamforming follows a geometrical method of delay estimation with a spatially constant speed-of-sound (SoS) of 1540 m/s throughout the medium irrespective of the tissue in-homogeneity. This approximation leads to errors in delay estimations that accumulate with depth and degrades the resolution, contrast and overall accuracy of the US image. In this work, we propose a fast marching based DAS for focused transmissions which leverages the approximate SoS map to estimate the refraction corrected propagation delays for each pixel in the medium. The proposed approach is validated qualitatively and quantitatively for imaging depths of upto ~ 11 cm through simulations, where fat layer induced aberration is employed to alter the SoS in the medium. To the best of authors' knowledge, this is the first work considering the effect of SoS on image quality for deeper imaging.Comment: 5 pages, 4 figure

Phase estimation methods and their application to holographic interferometry

Phase of the interference fringe pattern is known to convey important information in optical metrology. Typically, phase measurement using temporal techniques involves incorporating a piezoelectric device (PZT) in one arm of the interferometer for shifting the relative phase between the two interference beams. Although the precision in the measurement of phase achieved by this technique is one hundredth of the wavelength, the error arising due to the phase shifter itself is one of the potential bottlenecks in the successful measurement of the parameter of interest. The measurement process is also very sensitive to other systematic and random sources of errors that we may encounter during the experiment. To address these concerns, several algorithms have been proposed, but they have met with limited success as they allow only a limited number of error sources influencing the measurements to be minimized. The problem is exacerbated further when it comes to accommodating multiple PZTs in an optical configuration, such as, in holographic moiré. Incorporation of two PZTs is essential for the simultaneous estimation of multiple phase information in holographic moiré, such as, those corresponding to out-of-plane and in-plane displacement components. Recent introduction of high resolution methods in holographic moiré for the estimation of multiple phase information has been found to exhibit constraints while operating outside the linear region of the response of the piezoelectric device to the applied voltage. This research thesis thus addresses a significant issue of measuring phase efficiently in the presence of nonlinear response of the PZT to the applied voltage and at the same time contributes to compensating several other systematic sources of errors. For this we have designed methods based on signal processing approaches which have reputation of robust performers in the presence of random noise. The thesis presents simulation and experimental verification of the proposed methods to show their feasibility in practical situations. To the best of our knowledge, this is one of the first times that an attempt has been made to provide a robust signal processing approach for the estimation of multiple phase information in a topic of extreme significance such as that of optical metrology

High-resolution frequency estimation technique for recovering phase distribution in interferometers

An integral approach to phase measurement is presented. First, the use of a high-resolution technique for the pixelwise detection of phase steps is proposed. Next, the robustness of the algorithm that is developed is improved by incorporation of a denoising procedure during spectral estimation. The pixelwise knowledge of phase steps is then applied to the Vandermonde system of equations for retrieval of phase values at each pixel point. Conceptually, our proposal involves the design of an annihilating filter that has zeros at the frequencies associated with the polynomial that describes the fringe intensity. The parametric estimation of this annihilating filter yields the desired spectral information embedded in the signal, which in our case represents the phase steps. The proposed method offers the advantage of extracting the interference phase of nonsinusoidal waveforms in the presence of miscalibration error of the piezoelectric transducer. In addition, in contrast to previously reported methods, this method does not require the application of selective phase steps between data frames for nonsinusoidal waveforms. © 2005 Optical Society of America OCIS codes: 120.3180, 120.5050. Phase shifting has now become a well-established technique in optical interferometry for the detection of interference phase. The technique functions b

Accurate nonlinear phase step estimation in phase shifting interferometry

We propose a new method for the accurate estimation of nonlinear response of the PZT to the applied voltage. The method uses discrete chirp Fourier transform for the coarse estimation followed by a fine search method for the accurate estimation of the phase step and nonlinearity. The method can be extended to the cases of extraction of multiple phases in the configurations involving multiple PZTs such as holographic moire in the presence of nonlinearity. The robustness of the proposed method is verified by comparing with Cramer-Rao lower bound. Experimental results prove the method's feasibility. (c) 2006 Elsevier B.V. All rights reserved

Generalized linear prediction method in phase-shifting interferometry in the presence of noise

The effectiveness of phase-shifting interferometry (PSI) techniques employing piezoelectric device PZT in the estimation of phase depends largely on the accuracy with which the phase shifts are imparted to the device and the noise influencing the measurement. Several effective algorithms have been proposed to compute the phase shifts imparted to the device and subsequently obtain the phase using least-squares estimation technique. In this paper, we propose a generalized approach, which accurately estimates the phase shifts in the presence of noise. The method is based on the idea of linear prediction and explores the fact that sampling more data frames yields a reliable phase step estimate in a least-squares sense. We also compare our method with a commonly used generalized phase-shifting method based on histogram analysis and show that our proposed approach is highly effective. We also present simulation and experimental validations of our proposed method. (c) 2007 Elsevier Ltd. All rights reserved

Cramér-Rao estimation of error limits for diffuse optical tomography with spatial prior information

Cramér-Rao Bounds (CRB) for the expected variance in the parameter space were examined for Diffuse Optical Tomography (DOT), to define the lower bound (CRLB) of an ideal system. The results show that the relative standard deviation in the optical parameter estimate follows an inverse quadratic function with respect to signal to noise ratio (SNR). The CRLB was estimated for three methods of including spatial constraints. The CRLB estimate decreased by a factor of 10 when parameter reduction using spatial constraints (hard-priors) was enforced whereas, inclusion of spatial-priors in the regularization matrix (soft-priors) decreased the CRLB estimate only by a factor of 4. The maximum reduction in variance from the use of spatial-priors, occurred in the background of the imaging domain as opposed to localized target regions. As expected, the variance in the recovered properties increased as the number of parameters to be estimated increased. Additionally, increasing SNR beyond a certain point did not influence the outcome of the optical property estimation when prior information was available.</p

Three-Dimensional optical tomographic imaging of supersonic jets through inversion of phase data obtained through the transport-of-intensity equation

We report experimental results of quantitative imaging in supersonic circular jets by using a monochromatic light probe. An expanding cone of light interrogates a three-dimensional volume of a supersonic steady-state flow from a circular jet. The distortion caused to the spherical wave by the presence of the jet is determined through our measuring normal intensity transport. A cone-beam tomographic algorithm is used to invert wave-front distortion to changes in refractive index introduced by the flow. The refractive index is converted into density whose cross sections reveal shock and other characteristics of the flow

Three-Dimensional Optical Tomographic Imaging of Supersonic Jets through Inversion of Phase Data Obtained through the Transport-of-Intensity Equation

We report experimental results of quantitative imaging in supersonic circular jets by using a monochromatic light probe. An expanding cone of light interrogates a three-dimensional volume of a supersonic steady-state flow from a circular jet. The distortion caused to the spherical wave by the presence of the jet is determined through our measuring normal intensity transport. A cone-beam tomographic algorithm is used to invert wave-front distortion to changes in refractive index introduced by the flow. The refractive index is converted into density whose cross sections reveal shock and other characteristics of the flow